ABSTRACT Biological tissues are heterogeneous, particularly at a microscopic scale (e.g., ~10?m). The degree of tissue heterogeneity plays a very important role in tissue characterization, disease diagnosis, and monitoring treatment efficacy. In cancer, for example, intra-tumor heterogeneity has been identified as one of the most important factors in cancer staging and individualized treatment, as demonstrated in a number of recent papers in high-impact journals. Tissue heterogeneity arises from a variety of origins, such as genetics, epigenetics, physiology, and pathology, all of which lead to structural heterogeneity at a specific spatial scale. Studying tissue structural heterogeneity, therefore, can provide a unique avenue to probe the underlying biological processes. Current spatial resolution for human MRI, unfortunately, is far from adequate to visualize tissue structural heterogeneity at a microscopic level (e.g., ~5-50 ?m). Efforts to further improve the resolution face formidable technical challenges. An alternative strategy is to use the present spatial resolution, but focus on extracting sub-voxel information by linking a macroscopic voxel-level measurement to a microscopic intra-voxel physical process that reflects tissue structural heterogeneity. Using a novel diffusion model based on fractional order calculus (FROC), our group, echoed by others, has observed an increasing number of evidences suggesting a link between a macroscopic diffusion parameter and microscopic intra-voxel tissue heterogeneity. The overarching goal of the proposed project is to further develop and validate this promising diffusion imaging technique, and demonstrate that a set of FROC parameters can enable characterization of intra-voxel tissue heterogeneity in human subjects. The scientific premise of the project is that microstructural heterogeneity is an important tissue feature and that advanced diffusion MRI based on the FROC model can non-invasively assess microstructural heterogeneity, leading to new imaging markers. Our central hypothesis is that diffusion behavior in tissues at high b-values can be characterized by a heterogeneous diffusion process, and the degree of diffusion heterogeneity can be directly linked to intra-voxel tissue structural heterogeneity. The project has four Specific Aims. First, we will optimize a high-resolution diffusion imaging technique to enable accurate measurement of intra-voxel diffusion heterogeneity. Second, we will generalize the FROC diffusion model to account for intra-voxel diffusion heterogeneity not only spatially but also temporally. Third, using the techniques in the first two aims, we will demonstrate the possible relationship between MRI-based intra-voxel diffusion heterogeneity and histology-based structural heterogeneity on postmortem human brains with glioma. Finally, we will extend the demonstration to in vivo studies on sixty brain tumor patients using stereotactic biopsies. Taking together, the project will address a significant unmet need that is of great importance in biological sciences and clinical medicine, especially cancer.